Carole King and James Taylor do have children but not together.
They share their children with their respective spouses and partners.
Carole has four children, namely Louise Goffin, Levi Larkey, Sherry Goffin, and Molly Larkey whom she shares with her former husbands.
Similarly, James also has four children, namely Henry Taylor, Ben Taylor, Sally Taylor, Rufus Taylor. He shares his children with his ex-wife and his current wife.